1. Field of the Invention
The present invention relates to an apparatus for controlling the air-fuel ratio of a multicylinder internal combustion engine.
2. Description of the Related Art
Internal combustion engines having a multiplicity of cylinders, such as V-type 6-cylinder engines, V-type 8-cylinder engines, or in-line 6-cylinder engines, suffer structural limitations that make it difficult to combine exhaust gases generated by the combustion of an air-fuel mixture in the cylinders in a region close to the cylinders. Therefore, such multicylinder internal combustion engines generally have an exhaust system including relatively long auxiliary exhaust passages that extend separately from respective cylinder groups into which the cylinders are grouped. The auxiliary exhaust passages have downstream ends joined to a main exhaust passage which is shared by all the cylinders. In the exhaust system, exhaust gases from the cylinders of the cylinder groups are combined and discharged into the auxiliary exhaust passages near the cylinder groups, and then introduced from the auxiliary exhaust passages as combined exhaust gases into the main exhaust passage.
FIGS. 15 through 17 of the accompanying drawings schematically show respective V-type engines 1 each having two cylinder groups 3, 4 disposed one on each side of an output shaft, i.e., crankshaft, 2. Each of the cylinder groups 3, 4 comprises a plurality of cylinders 5 juxtaposed closely to each other in the axial direction of the output shaft 2. If the V-type engine 1 is a V-type 6-cylinder engine, then each of the cylinder groups 3, 4 comprises three cylinders. If the V-type engine 1 is a V-type 8-cylinder engine, then each of the cylinder groups 3, 4 comprises four cylinders.
The V-type engine 1 has an exhaust system including an auxiliary exhaust pipe, i.e., an auxiliary exhaust passage, 6 extending from the cylinder group 3 for receiving exhaust gases produced in the cylinders 5 of the cylinder group 3 and combined by an exhaust manifold near the cylinder group 3, and an auxiliary exhaust pipe, i.e., an auxiliary exhaust passage, 7 extending from the cylinder group 4 for receiving exhaust gases produced in the cylinders 5 of the cylinder group 4 and combined by an exhaust manifold near the cylinder group 4. The auxiliary exhaust pipes 6, 7 have downstream ends connected to a main exhaust pipe, i.e., a main exhaust passage, 8.
FIG. 18 of the accompanying drawings schematically shows an in-line 6-cylinder engine 101 having six cylinders 103 juxtaposed in the axial direction of an output shaft, i.e., a crankshaft, 102. The cylinders 103 are grouped into a right cylinder group 104 of three closely positioned cylinders 103 and a left cylinder group 105 of three closely positioned cylinders 103. The in-line 6-cylinder engine 101 has an exhaust system including auxiliary exhaust pipes, or auxiliary exhaust passages, 106, 107 extending respectively from the cylinder groups 103, 104. The auxiliary exhaust pipes 106, 107 have downstream ends connected to a main exhaust pipe, i.e., a main exhaust passage, 108.
In the above multicylinder internal combustion engines whose exhaust system includes the auxiliary exhaust passages associated with the respective cylinder groups and the main exhaust passage to which the auxiliary exhaust passages are connected in common, catalytic converters, such as three-way catalytic converters, for purifying exhaust gases are generally arranged in the following layouts:
In FIG. 15, catalytic converters 9, 10 are connected to the respective auxiliary exhaust pipes 6, 7. In FIG. 16, catalytic converters 9, 10, 11 are connected respectively to the auxiliary exhaust pipes 6, 7 and the main exhaust pipe 8. In FIG. 17, a catalytic converter 11 is connected to the main exhaust pipe 8 only.
The above catalytic converter layouts are applicable to not only the exhaust systems of the V-type engines 1 shown in FIGS. 15 through 17, but also the exhaust system of the in-line 6-cylinder engine 101 shown in FIG. 18.
It is more important than ever for exhaust gas purifying systems for use with not only the above multicylinder internal combustion engines, but also other internal combustion engines, to have catalytic converters with a reliable exhaust gas purifying capability for effective environmental protection.
In order to achieve a desired exhaust gas purifying capability of a catalytic converter irrespective of deterioration of the catalytic converter, the applicant of the present application has proposed a system having an O2 sensor disposed downstream of the catalytic converter for detecting the concentration of a certain component, e.g., the concentration of oxygen, in exhaust gases that have passed through the catalytic converter. The proposed system controls the air-fuel ratio of a mixture of air and fuel combusted by an internal combustion engine for converging the output of the O2 sensor, i.e., the detected oxygen concentration, to a predetermined target value, i.e., a constant value. See, for example, Japanese laid-open patent publication No. 11-93741 or U.S. Pat. No. 6,082,099, for details.
According to the disclosed arrangement, the O2 sensor is disposed downstream of the catalytic converter in an exhaust system, such as for an in-line 4-cylinder engine, wherein exhaust gases from all the cylinders are combined and introduced into a single exhaust pipe near the engine and the catalytic converter is connected to the single exhaust pipe only. A target air-fuel ratio, more precisely a target value for the air-fuel ratio represented by the oxygen concentration in the exhaust gases in a region where the exhaust gases from all the cylinders are combined, is determined for an air-fuel mixture combusted by the engine in order to converge the output of the O2 sensor to the predetermined target value, and the air-fuel ratio of the air-fuel mixture combusted in the cylinders of the engine is controlled depending on the target air-fuel ratio.
In view of the above technical background, there have been proposed exhaust systems for use with multicylinder internal combustion engines having auxiliary exhaust passages associated with respective cylinder groups. Each of the proposed exhaust systems controls the air-fuel ratio of the internal combustion engine in order to achieve a desired purifying capability of catalytic converters connected to the auxiliary exhaust passages and the main exhaust passage. Those proposed exhaust systems will be described below.
If the catalytic converters 9, 10 are connected to the respective auxiliary exhaust pipes 6, 7 as shown in FIG. 15, then in order to achieve a total purifying capability of the catalytic converters 9, 10, an O2 sensor 12 is mounted on the main exhaust pipe 8 near an upstream end thereof where the auxiliary exhaust pipes 6, 7 are joined, and the air-fuel ratios of the air-fuel mixtures combusted in the cylinder groups 3, 4 of the engine 1 are controlled in order to converge the output of the O2 sensor 12 to the predetermined target value.
If the catalytic converters 9, 10, 11 are connected respectively to the auxiliary exhaust pipes 6, 7 and the main exhaust pipe 8, as shown in FIG. 16, then in order to achieve a total purifying capability of the catalytic converters 9, 10, 11, an O2 sensor 12 is mounted on the main exhaust pipe 8 downstream of the catalytic converter 11, and the air-fuel ratio of the air-fuel mixture combusted in the cylinder groups 3, 4 of the engine 1 is controlled in order to converge the output of the O2 sensor 12 to the predetermined target value.
If the catalytic converter 11 is connected to the main exhaust pipe 8 only, as shown in FIG. 17, then in order to achieve a purifying capability of the catalytic converter 11, an O2 sensor 12 is mounted on the main exhaust pipe 8 downstream of the catalytic converter 11, and the air-fuel ratio of the air-fuel mixture combusted in the cylinder groups 3, 4 of the engine 1 is controlled in order to converge the output of the O2 sensor 12 to the predetermined target value.
Generally, due to differences in length and shape between the auxiliary exhaust pipes 6, 7 and also differences in characteristics between the catalytic converters 9, 10 connected to the auxiliary exhaust pipes 6, 7, response characteristics of changes in the output of the O2 sensor 12 with respect to changes in the air-fuel ratio of the air-fuel mixture combusted in the cylinder groups 3, 4 differ between the auxiliary exhaust pipe 6, i.e., the cylinder group 3, and the auxiliary exhaust pipe 8, i.e., the cylinder group 4.
For performing the control process to converge (set) the output of the O2 sensor 12 to the predetermined target value with as high stability as possible, it is desirable to determine target air-fuel ratios for the respective cylinder groups 3, 4 and control the air-fuel ratios of the air-fuel mixtures combusted in the cylinder groups 3, 4 depending on the respective target air-fuel ratios.
To determine target air-fuel ratios for the respective cylinder groups 3, 4, however, it is necessary to recognize an exhaust system, upstream of the O2 sensor 12, which comprises the auxiliary exhaust pipes 6, 7 and the catalytic converters 9, 10, as a 2-input, 1-output system which generates the output of the O2 sensor 12 from the air-fuel ratios of the air-fuel mixtures combusted in the cylinder groups 3, 4. Consequently, determining target air-fuel ratios for the respective cylinder groups 3, 4 requires a complex model and a complex computing algorithm for the 2-input, 1-output system. The complex model and the complex computing algorithm tend to cause a modeling error and accumulated computation errors, which make it difficult to determine appropriate target air-fuel ratios.
It is therefore an object of the present invention to provide an air-fuel ratio control apparatus for a multicylinder internal combustion engine having as many auxiliary exhaust passages as the number of cylinder groups, the air-fuel ratio control apparatus being capable of appropriately controlling air-fuel ratios of the respective cylinder groups for converging an output of an O2 sensor that is disposed in a main exhaust passage downstream of a catalytic converter according to a relatively simple process without the need for a complex model and a complex algorithm.
Another object of the present invention is to provide an air-fuel ratio control apparatus for a multicylinder internal combustion engine, which is capable of performing a control process of converting an output of an exhaust gas sensor to a target value accurately and stably and hence of reliably achieving a desired purifying capability of a catalytic converter.
To achieve the above objects, there is provided in accordance with the present invention an apparatus for controlling the air-fuel ratio of a multicylinder internal combustion engine having all cylinders divided into a plurality of cylinder groups and an exhaust system including a plurality of auxiliary exhaust passages for discharging exhaust gases produced when an air-fuel mixture of air and fuel is combusted from the cylinder groups, respectively, a main exhaust passage joining the auxiliary exhaust passages together at downstream sides thereof, an exhaust gas sensor mounted in the main exhaust passage for detecting the concentration of a given component in the exhaust gases flowing through the main exhaust passage, and a catalytic converter connected to the auxiliary exhaust passages and/or the main exhaust passage upstream of the exhaust gas sensor, so that the air-fuel ratio of the air-fuel mixture combusted in each of the cylinder groups is controlled to converge an output from the exhaust gas sensor to a predetermined target value. The apparatus comprises a plurality of air-fuel ratio sensors mounted respectively in the auxiliary exhaust passages upstream of the catalytic converter, for detecting the air-fuel ratio of the air-fuel mixture combusted in each of the cylinder groups, the exhaust system including an object exhaust system disposed upstream of the exhaust gas sensor and including the auxiliary exhaust passages and the catalytic converter, the object exhaust system being equivalent to a system for generating an output of the exhaust gas sensor from a combined air-fuel ratio determined by combining the values of air-fuel ratios of air-fuel mixtures combusted by the cylinder groups, respectively, according to a filtering process of the mixed model type, and target combined air-fuel ratio data generating means for sequentially generating target combined air-fuel ratio data representing a target value for the combined air-fuel ratio which is required to converge the output from the exhaust gas sensor to the predetermined target value with the system equivalent to the object exhaust system serving as an object to be controlled. The apparatus also has target air-fuel ratio data generating means for sequentially generating target air-fuel ratio data from the target combined air-fuel ratio data generated by the target combined air-fuel ratio data generating means according to a predetermined converting process based on characteristics of a filtering process identical to the filtering process of the mixed model type, the target air-fuel ratio data representing a target air-fuel ratio for the air-fuel mixture combusted in each of the cylinder groups, the target air-fuel ratio being shared by the cylinder groups, the target combined air-fuel ratio data being produced by subjecting the target air-fuel ratio data to the filtering process, and air-fuel ratio manipulating means for manipulating the air-fuel ratio of the air-fuel mixture combusted in each of the cylinder groups in order to converge an output of each of the air-fuel ratio sensors to the target air-fuel ratio represented by the target air-fuel ratio data generated by the target air-fuel ratio data generating means.
With the above arrangement, the combined air-fuel ratio is introduced which is produced by combining the values, detected by the respective air-fuel ratio sensors, of the air-fuel ratios of the air-fuel mixtures combusted in the cylinder groups according to the filtering process of the mixed model type. Therefore, the object exhaust system of the exhaust system of the multicylinder internal combustion engine can be regarded as being equivalent to a system for generating the output of the exhaust gas sensor from the combined air-fuel ratio. Stated otherwise, the object exhaust system can be regarded as being equivalent to a 1-input, 1-output system (hereinafter referred to as xe2x80x9cequivalent exhaust systemxe2x80x9d) for being supplied with the combined air-fuel ratio as an input quantity and outputting the output of the exhaust gas sensor as an output quantity.
With the equivalent exhaust system introduced, in order to control the output of the exhaust gas sensor which is the output quantity from the equivalent exhaust system at the predetermined target value, the combined air-fuel ratio may be manipulated as a control input to the equivalent exhaust system. According to the present invention, the target combined air-fuel ratio data generating means sequentially generates target combined air-fuel ratio data representing a target value for the combined air-fuel ratio which is required to converge the output from the exhaust gas sensor to the predetermined target value with the equivalent exhaust system serving as an object to be controlled.
The target combined air-fuel ratio data generating means may generate only the target combined air-fuel ratio data as a single control input to the equivalent object system. Therefore, the target combined air-fuel ratio data generating means can generate the target combined air-fuel ratio data using the algorithm of a relatively simple feedback control process, e.g., a PID control process, without using a complex model of the equivalent object system.
The target combined air-fuel ratio data generated by the target combined air-fuel ratio data generating means may represent the value of the target combined air-fuel ratio itself. However, the target combined air-fuel ratio data may represent the difference between the value of the target combined air-fuel ratio and a predetermined reference air-fuel ratio, e.g., a stoichiometric air-fuel ratio.
When the target combined air-fuel ratio data is thus generated, the target combined air-fuel ratio represented by the target combined air-fuel ratio data is equal to the values of the target air-fuel ratios of the air-fuel mixtures combusted in the respective cylinder groups which are combined by a filtering process identical to the filtering process of the mixed model type, according to the definition of the combined air-fuel ratio. Because of the characteristics of the filtering process of the mixed model type, the target air-fuel ratio for each of the cylinder groups may be shared by all the cylinder groups. With the value of the target combined air-fuel ratio being determined, a target air-fuel ratio for each of the cylinder groups can be determined from the target combined air-fuel ratio according to a process that is a reversal of the filtering process.
According to the present invention, the target air-fuel ratio data generating means sequentially generates the target air-fuel ratio data from the target combined air-fuel ratio data generated by the target combined air-fuel ratio data generating means according to a predetermining converting process, which is a process that is a reversal of the filtering process, based on characteristics of the filtering process identical to the filtering process of the mixed model type, the target air-fuel ratio data representing a target air-fuel ratio for the air-fuel mixture combusted in each of the cylinder groups, the target air-fuel ratio being shared by the cylinder groups, the target combined air-fuel ratio data being produced by subjecting the target air-fuel ratio data to the filtering process.
Therefore, it is possible to obtain a target air-fuel ratio for each of the cylinder groups which is required to converge the output of the exhaust gas sensor to the predetermined target value.
As with the target combined air-fuel ratio data, the target air-fuel ratio data may represent the value of the target air-fuel ratio itself. However, the target air-fuel ratio data may represent the difference between the value of the target air-fuel ratio and a predetermined reference air-fuel ratio, e.g., a stoichiometric air-fuel ratio.
According to the present invention, the air-fuel ratio manipulating means manipulates the air-fuel ratio of the air-fuel mixture combusted in each of the cylinder groups in order to converge an output of each of the air-fuel ratio sensors, i.e., the detected value of the air-fuel ratio of the air-fuel mixture combusted in each of the cylinder groups, to the target air-fuel ratio represented by the target air-fuel ratio data thus generated. Thus, the combined air-fuel ratio that is the input quantity to the equivalent exhaust system is manipulated into the target combined air-fuel ratio represented by the target combined air-fuel ratio data, and the output of the exhaust gas sensor is converted to the predetermined target value.
According to the present invention, as described above, the target air-fuel ratio for each of the cylinder groups can appropriately be determined in order to converge the output of the exhaust gas sensor disposed downstream of the catalytic converter to the predetermined target value according to a relatively simple process without the need for a complex model and algorithm. By manipulating the air-fuel ratio of each of the cylinder groups in order to converge the output of each of the air-fuel ratio sensors which detects the air-fuel ratio of the air-fuel mixture combusted in each of the cylinder groups, to the target air-fuel ratio, the control process of converging the output of the exhaust gas sensor to the predetermined target value can suitably be performed. As a result, the catalytic converter disposed in each of the auxiliary exhaust passages or the main exhaust passage upstream of the exhaust sensor can have a good purifying capability.
For the catalytic converter disposed upstream of the exhaust sensor to have an optimum purifying capability, it is preferable that the exhaust gas sensor comprise an O2 sensor and the target value for the output of the exhaust gas sensor be a constant value.
The filtering process of the mixed model type comprises a filtering process for obtaining the combined air-fuel ratio in each given control cycle by combining a plurality of time-series values of the air-fuel ratio of the air-fuel mixture combusted in each of the cylinder groups in a control cycle earlier than the control cycle, according to a linear function having the time-series values as components thereof.
The filtering process using the linear function allows a combined air-fuel ratio to be defined which is suitable for determining the target air-fuel ratio for each of the cylinder groups.
The linear function which has, as its components, a plurality of time-series values of the air-fuel ratio of the air-fuel mixture combusted in each of the cylinder groups is a linear combination of those time-series values, for example. In this case, the filtering process obtains a weighted mean value of the time-series values as the combined air-fuel ratio.
When the filtering process of the mixed model type is determined by the linear function, the target combined air-fuel ratio data in each given control cycle is obtained by a linear function which employs time-series data of the target air-fuel ratio data earlier than the control cycle as components of the linear function. Therefore, the target air-fuel ratio data generating means can generate target air-fuel ratio data in each given control cycle from the target combined air-fuel ratio data generated by the target combined air-fuel ratio data generating means, according to a predetermined operating process determined by the linear function.
More specifically, the target air-fuel ratio data in each control cycle may be determined using the target combined air-fuel ratio data in the control cycle and the target air-fuel ratio data in a past control cycle prior to the control cycle.
The target combined air-fuel ratio data may be generated by a feedback control process, such as a PID control process, which does not need a model of the object to be controlled. However, since the object exhaust system includes the catalytic converter, a change in the output of the exhaust gas sensor which serves as the output quantity to the equivalent exhaust system, in response to a change in the input quantity to the equivalent exhaust system that is equivalent to the object exhaust system, is liable to be affected by a response delay caused by the catalytic converter.
According to the present invention, therefore, the target combined air-fuel ratio data generating means comprises means for generating the target combined air-fuel ratio data in order to converge the output of the exhaust gas sensor to the predetermined target value according to an algorithm of a feedback control process constructed based on a predetermined model of the equivalent exhaust system which is defined as a system for generating data representing the output of the exhaust gas sensor with at least a response delay from the combined air-fuel ratio data representing the combined air-fuel ratio.
By thus generating the target combined air-fuel ratio data using the algorithm of the feedback control process constructed based on the model of the equivalent exhaust system in view of the response delay thereof, the effect of the response delay due to the catalytic converter included in the object exhaust system is appropriately compensated for, generating target combined air-fuel ratio data suitable for converting the output of the exhaust gas sensor to the predetermined target value. Inasmuch as the equivalent exhaust system is a 1-input, 1-output system, the equivalent exhaust system can be constructed of a simple arrangement.
In the above model, the combined air-fuel ratio data should preferably represent the difference between an actual combined air-fuel ratio and a predetermined reference air-fuel ratio, and the data representing the output of the exhaust gas sensor should preferably represent the difference between an actual output from the exhaust gas sensor and the predetermined target value for the purposes of increasing the ease with which to construct the algorithm of the feedback control process and the reliability of the target combined air-fuel ratio data generated using the algorithm. In this case, the target combined air-fuel ratio data represents the difference between an actual target combined air-fuel ratio and the predetermined reference air-fuel ratio, i.e., a target value for the difference between the combined air-fuel ratio and the reference air-fuel ratio.
If the algorithm of the feedback control process performed for the target combined air-fuel ratio data generating means to generate the target combined air-fuel ratio data is constructed based on the model of the equivalent exhaust system, then the algorithm of the feedback control process should preferably comprise an algorithm of a sliding mode control process.
Particularly, the sliding mode control process should preferably comprise an adaptive sliding mode control process.
Specifically, the sliding mode control process has such characteristics that it generally has high control stability against disturbances. By generating the target combined air-fuel ratio data using the algorithm of the sliding mode control process, the reliability of the target combined air-fuel ratio data is increased, and hence the stability of the control process of converging the output of the exhaust gas sensor to the target value is increased.
The adaptive sliding mode control process incorporates an adaptive control law (adaptive algorithm) for minimizing the effect of a disturbance, in a normal sliding mode control process. Therefore, the target combined air-fuel ratio data is made highly reliable.
More specifically, the sliding mode control process uses a function referred to as a switching function constructed using the difference between a controlled quantity (the output of the exhaust gas sensor in this invention) and its target value, and it is important to converge the value of the switching function to xe2x80x9c0xe2x80x9d. According to the normal sliding mode control process, a control law referred to as a reaching control law is used to converge the value of the switching function to xe2x80x9c0xe2x80x9d. However, due to the effect of a disturbance, it may be difficult in some situations to provide sufficient stability in converging the value of the switching function to xe2x80x9c0xe2x80x9d only with the reaching control law. According to the adaptive sliding mode control process, in order to converge the value of the switching function to xe2x80x9c0xe2x80x9d while minimizing the effect of disturbances, the adaptive control law (adaptive algorithm) is used in addition to the reaching control law. By using the algorithm of the adaptive sliding mode control process, it is possible to converge the value of the switching function highly stably to xe2x80x9c0xe2x80x9d, and hence converge the output of the exhaust gas sensor to the predetermined target value with high stability.
As described above, the algorithm of the feedback control process comprises the algorithm of the sliding mode control process (including the adaptive sliding mode control process). Preferably, the algorithm of the sliding mode control process employs, as a switching function for the sliding mode control process, a linear function having, as components, a plurality of time-series data of the difference between the output of the exhaust gas sensor and the predetermined target value.
In the sliding mode control process, the switching function used thereby usually comprises a controlled quantity and a rate of change thereof. The rate of change of the controlled quantity is generally difficult to detect directly, and is often calculated from a detected value of the controlled quantity. The calculated value of the rate of change of the controlled quantity tends to suffer an error.
According to the present invention, the switching function for the sliding mode control process comprises a linear function having, as components, a plurality of time-series data of the difference between the output of the exhaust gas sensor and the predetermined target value. Therefore, the algorithm for generating the target combined air-fuel ratio data can be constructed without the need for the rate of change of the output of the exhaust gas sensor. Consequently, the reliability of the generated target combined air-fuel ratio data is increased.
With the switching function thus constructed, the algorithm of the sliding mode control process generates target combined air-fuel ratio data so as to converge the values of the time-series data of the difference between the output of the exhaust gas sensor and the predetermined target value to xe2x80x9c0xe2x80x9d.
In order to generate target combined air-fuel ratio data as described above, the algorithm of the feedback control process based on the model of the equivalent exhaust system including the algorithm of the sliding mode control process is employed. The model should preferably comprise a model which expresses a behavior of the equivalent exhaust system with a discrete time system, though it may comprise a model which expresses a behavior of the equivalent exhaust system with a continuous time system.
With the behavior of the equivalent exhaust system being expressed by the discrete time system, the algorithm of the feedback control process can be constructed easily, and can be made suitable for computer processing.
The model which expresses the behavior of the equivalent exhaust system with the discrete time system may comprise a model which expresses data representing the output of the exhaust gas sensor in each given control cycle with data representing the output of the exhaust gas sensor in a past control cycle prior to the control cycle and the combined air-fuel ratio data.
The model thus constructed can appropriately express the behavior of the equivalent exhaust system.
The data representing the output of the exhaust gas sensor in the past control cycle is a so-called autoregressive term, and is related to a response delay of the equivalent exhaust system.
With the model of the equivalent exhaust system comprising the model of the discrete time system, as described above, the apparatus should further comprise first filtering means for sequentially determining the combined air-fuel ratio data by effecting a filtering process identical to the filtering process of the mixed model type on the output of each of the air-fuel ratio sensors, and identifying means for sequentially identifying a value of a parameter to be set of the model using the combined air-fuel ratio data determined by the first filter means and the data representing the output of the exhaust gas sensor, wherein the algorithm of the feedback control process performed by the target combined air-fuel ratio data generating means comprises an algorithm for generating the target combined air-fuel ratio data using the value of the parameter identified by the identifying means.
The model has parameters to be set to a certain value in describing its behavior. For example, if the model is a model which expresses the data representing the output of the exhaust gas sensor in each given control cycle with data representing the output of the exhaust gas sensor in a past control cycle prior to the control cycle and the combined air-fuel ratio data, then coefficient parameters relative respectively to the data representing the output of the exhaust gas sensor in the past control cycle and the combined air-fuel ratio data are included in the parameters of the model.
According to the algorithm of the feedback control process constructed based on the model, the target combined air-fuel ratio data is generated using the parameters of the model. For increasing the reliability of the target combined air-fuel ratio data, it is preferable to identify the values of the parameters of the model on a real-time basis depending on the actual behavior of the equivalent exhaust system, which is based on the actual behavioral characteristics of the object exhaust system and often tends to change with time.
When the combined air-fuel ratio data is determined by effecting the filtering process identical to the filtering process of the mixed model type on the data representing the output of each of the air-fuel ratio sensors, the combined air-fuel ratio data corresponds to the detected value of the actual combined air-fuel ratio as the input quantity to the equivalent exhaust system. In the model which expresses the equivalent exhaust system with the discrete time system, the combined air-fuel ratio data sequentially determined from the data representing the output of each of the air-fuel ratio sensors and the data representing the output of the exhaust gas sensor corresponding to the actual output quantity from the equivalent exhaust system are used to sequentially identify the parameters of the model depending on the actual behavior of the equivalent exhaust system.
Therefore, the apparatus of the present invention further includes the first filter means and the identifying means. The values of the parameters of the model are sequentially identified, and the target combined air-fuel ratio data is generated using the identified values of the parameters. It is thus possible to generate the target combined air-fuel ratio data depending on the actual behavior of the equivalent exhaust system based on the actual behavior, from time to time, of the object exhaust system. As a result, the reliability of the target combined air-fuel ratio data is increased, making it possible to accurately and stably converge the output of the exhaust gas sensor to the predetermined target value.
If the model is a model which expresses the data representing the output of the exhaust gas sensor in each given control cycle with data representing the output of the exhaust gas sensor in a past control cycle prior to the control cycle and the combined air-fuel ratio data, then the identifying means identifies at least one of the coefficient parameters, preferably all the coefficient parameters, relative respectively to the data representing the output of the exhaust gas sensor and the combined air-fuel ratio data.
The identifying means can sequentially identify the values of the parameters according to an algorithm, e.g., an identifying algorithm such as a method of least squares, a method of weighted least squares, a fixed gain method, a degressive gain method, a fixed tracing method, etc., constructed in order to minimize an error between the output of the exhaust gas sensor in the model and the actual output of the exhaust gas sensor.
In the apparatus for controlling the air-fuel ratio of the multicylinder internal combustion engine according to the present invention, the equivalent exhaust system may have a relatively long dead time, i.e., a time required until the value, at each time point, of the actual combined air-fuel ratio that is the input quantity to the equivalent exhaust system is reflected in the output of the exhaust gas sensor, because of the catalytic converter and the auxiliary exhaust pipes, which are relatively long, in the object exhaust system. With the equivalent exhaust system having such a dead time, then the stability of the control process of converging the output of the exhaust gas sensor to the predetermined target value would tend to be lowered if the target combined air-fuel ratio were generated to manipulate the air-fuel ratio for the cylinder groups without taking the data time into account.
According to the present invention, the further comprises estimating means for sequentially generating data representing an estimated value of the output of the exhaust gas sensor after a dead time according to an algorithm constructed based on a predetermined model of the equivalent exhaust system which is defined as a system for generating data representing the output of the exhaust gas sensor with a response delay and the dead time from the combined air-fuel ratio data representing the combined air-fuel ratio. The target combined air-fuel ratio data generating means comprises means for generating the target combined air-fuel ratio data in order to converge the output of the exhaust gas sensor to the predetermined target value according to an algorithm of a feedback control process constructed using the data generated by the estimating means.
Since the model of the equivalent exhaust system is determined in view of the response delay and dead time thereof, the estimating means can sequentially generate data representing an estimated value of the output of the exhaust gas sensor after the dead time according to the algorithm constructed based on the model.
The target combined air-fuel ratio data generating means generates the target combined air-fuel ratio data according to the algorithm of the feedback control process constructed using the data representing the estimated value of the output of the exhaust gas sensor. Therefore, it is possible to generate the target combined air-fuel ratio data suitable for compensating for the effect of the dead time of the equivalent exhaust system and converging the output of the exhaust gas sensor stably to the predetermined target value.
When the multicylinder internal combustion engine operates at a relatively low rotational speed, a system comprising the air-fuel ratio manipulating means and the multicylinder internal combustion engine, which system is basically considered to be a system for generating an actual combined air-fuel ratio corresponding to the target air-fuel ratio data from the target air-fuel ratio data, may have a relatively long dead time. In such a case, the stability of the control process of converging the output of the exhaust gas sensor to the predetermined target value would not be sufficiently high if only the effect of the dead time of the equivalent exhaust system were compensated for.
According to the present invention, the apparatus further comprises estimating means for sequentially generating an estimated value of the output of the exhaust gas sensor after a total dead time which is the sum of a dead time of the equivalent exhaust system and a dead time of a system comprising the air-fuel ratio manipulating means and the multicylinder internal combustion engine, according to according to an algorithm constructed based on a predetermined model of the equivalent exhaust system which is defined as a system for generating data representing the output of the exhaust gas sensor with a response delay and the dead time from the combined air-fuel ratio data representing the combined air-fuel ratio, and a predetermined model of the system (hereinafter referred to as xe2x80x9cair-fuel ratio manipulating systemxe2x80x9d) comprising the air-fuel ratio manipulating means and the multicylinder internal combustion engine which is defined as a system for generating the combined air-fuel ratio data with the dead time from the target combined air-fuel ratio data. The target combined air-fuel ratio data generating means comprises means for generating the target combined air-fuel ratio data in order to converge the output of the exhaust gas sensor to the predetermined target value according to an algorithm of a feedback control process constructed using the data generated by the estimating means.
Since the model of the equivalent exhaust system is determined in view of the response delay and dead time thereof and the model of the air-fuel ratio manipulating system is determined in view of the dead time thereof, the estimating means can sequentially generate data representing an estimated value of the output of the exhaust gas sensor after the total dead time, which represents the sum of the dead time of the equivalent exhaust system and the dead time of the air-fuel ratio manipulating system, according to the algorithm constructed based on those models. Because the effect of the response delay of the multicylinder internal combustion engine can be compensated for by the air-fuel ratio manipulating means, no problem arises if the response delay of the multicylinder internal combustion engine is taken into account in the model of the air-fuel ratio manipulating means.
The target combined air-fuel ratio data generating means generates the target combined air-fuel ratio data according to the algorithm of the feedback control process constructed using the data representing the estimated value of the output of the exhaust gas sensor. Therefore, it is possible to generate the target combined air-fuel ratio data suitable for compensating for the effect of the dead time of the equivalent exhaust system and the dead time of the air-fuel ratio manipulating system and converging the output of the exhaust gas sensor stably to the predetermined target value.
Irrespective whether the data representing the estimated value of the output of the exhaust gas sensor after the dead time of the equivalent exhaust system is generated or the data representing the estimated value of the output of the exhaust gas sensor after the total dead time representing the sum of the dead time of the equivalent exhaust system and the dead time of the air-fuel ratio manipulating system, the combined air-fuel ratio data represents the difference between an actual combined air-fuel ratio and a predetermined reference air-fuel ratio, and the data representing the output of the exhaust gas sensor represents the difference between an actual output from the exhaust gas sensor and the predetermined target value in the model of the equivalent exhaust model. Such an arrangement is effective to increase the ease with which to construct the algorithm for generating the data representing the estimated value of the output of the exhaust gas sensor and to increase the reliability of the data representing the estimated value of the output of the exhaust gas sensor using the algorithm. In this case, the data representing the estimated value of the output of the exhaust gas sensor represents the difference the estimated value of the output of the exhaust gas sensor and the predetermined target value
The estimating means can sequentially generate data representing an estimated value of the output of the exhaust gas sensor after the dead time of the equivalent exhaust system or the total data time representing the sum of the dead time of the equivalent exhaust system and the dead time of the air-fuel ratio manipulating system, basically according to the algorithm constructed using the target combined air-fuel ratio data, specifically, a plurality of time-series data of past values of the target combined air-fuel ratio data, generated by the target combined air-fuel ratio data generating means, and the data representing the output of the exhaust gas sensor, specifically, a plurality of time-series data of the data prior to the present cycle.
If the dead time of the air-fuel ratio manipulating system can be ignored, i.e., if the data representing the estimated value of the output of the exhaust gas sensor after the dead time of the equivalent exhaust system is generated, then the target combined air-fuel ratio data at each time point can basically be considered to be equal to the combined air-fuel ratio data representing the actual combined air-fuel ratio at the same time point.
If the air-fuel ratio manipulating system has a dead time, i.e., if the data representing the estimated value of the output of the exhaust gas sensor after the total data time representing the sum of the dead time of the equivalent exhaust system and the dead time of the air-fuel ratio manipulating system is generated, then the target combined air-fuel ratio data at each time point can basically be considered to be equal to the combined air-fuel ratio data representing the actual combined air-fuel ratio after the dead time of the equivalent exhaust system by the model of the air-fuel ratio manipulating system.
When the combined air-fuel ratio data is sequentially determined by effecting the filtering process identical to the filtering process of the mixed model type on the output of each of the air-fuel ratio sensors, the combined air-fuel ratio data corresponds to the detected value of the actual combined air-fuel ratio as the input quantity to the equivalent exhaust system.
In view of the relationship between the target combined air-fuel ratio data and the corresponding actual combined air-fuel ratio data, if the dead time of the air-fuel ratio manipulating system can be ignored, then the combined air-fuel ratio data determined as described above from the data representing the output of each of the air-fuel ratio sensors can be used instead of all target combined air-fuel ratio data used in the algorithm which uses the target combined air-fuel ratio data and the data representing the output of the exhaust gas sensor in order to generate the estimated value of the output of the exhaust gas sensor.
If the air-fuel ratio manipulating system has a dead time and the dead time is relatively short, or specifically, if the dead time is at most the same as the period for generating the target combined air-fuel ratio data, then the combined air-fuel ratio data determined from the data representing the output of each of the air-fuel ratio sensors can be used instead of all target combined air-fuel ratio data used in the above algorithm for generating the data representing the output of the exhaust gas sensor.
If the air-fuel ratio manipulating system has a dead time and the dead time is relatively long, or specifically, if the dead time is longer than the period for generating the target combined air-fuel ratio data, then the combined air-fuel ratio data determined from the data representing the output of each of the air-fuel ratio sensors can be used instead of some target combined air-fuel ratio data used in the above algorithm.
In the case where the estimating means sequentially generates the data representing the estimated value of the output of the exhaust gas sensor after the dead time of the equivalent exhaust system or the estimating means sequentially generates the data representing the estimated value of the output of the exhaust gas sensor after the total data time representing the sum of the dead time of the equivalent exhaust system and the dead time of the air-fuel ratio manipulating system, the apparatus further comprises first filtering means for sequentially determining the combined air-fuel ratio data by effecting a filtering process identical to the filtering process of the mixed model type on the output of each of the air-fuel ratio sensors. The algorithm performed by the estimating means comprises an algorithm for generating the data representing the estimated value of the output of the exhaust gas sensor using the data representing the output of the exhaust gas sensor and the combined air-fuel ratio data generated by the first filter means.
In the case where the estimating means sequentially generates the data representing the estimated value of the output of the exhaust gas sensor after the total data time representing the sum of the dead time of the equivalent exhaust system and the dead time of the air-fuel ratio manipulating system, the apparatus further comprises first filtering means for sequentially determining the combined air-fuel ratio data by effecting a filtering process identical to the filtering process of the mixed model type on the output of each of the air-fuel ratio sensors. The algorithm performed by the estimating means comprises an algorithm for generating the data representing the estimated value of the output of the exhaust gas sensor using the data representing the output of the exhaust gas sensor and the combined air-fuel ratio data generated by the first filter means.
As described above, the algorithm for the estimating means to generate the data representing the estimated value of the output of the exhaust gas sensor uses the combined air-fuel ratio data generated by the first filter means, i.e., the data corresponding to the detected value of the actual combined air-fuel ratio. Therefore, even if the actual combined air-fuel ratio suffers an error due to a disturbance with respect to the target combined air-fuel ratio data, the estimating means can generate the data representing the estimated value of the output of the exhaust gas sensor in a manner to take the effect of the disturbance into account. Consequently, the reliability of the data representing the estimated value is increased. Thus, the target combined air-fuel ratio data generating means can generate the target combined air-fuel ratio data while appropriately compensating for the dead time of the equivalent exhaust system and the dead time of the air-fuel ratio manipulating system according to the algorithm of the feedback control process that is constructed using the data representing the estimated value.
In the above apparatus with the above estimating means, the air-fuel ratio manipulating means does not always need to manipulate the air-fuel ratio of the air-fuel mixture in each of the cylinder groups according to the target air-fuel ratio represented by the target air-fuel ratio data that is generated by the target combined air-fuel ratio data generating means from the target combined air-fuel ratio data, but may manipulate the air-fuel ratio of the air-fuel mixture in each of the cylinder groups according to a target air-fuel ratio other than the target air-fuel ratio data generated by the target combined air-fuel ratio data generating means, depending on operating conditions of the multicylinder internal combustion engine, e.g., when the internal combustion engine operates with the supply of fuel being cut off or operates to meet a large output power requirement.
If the air-fuel ratio manipulating means comprises means for manipulating the air-fuel ratio of the air-fuel mixture combusted in each of the cylinder groups depending on a target air-fuel ratio other than the target air-fuel ratio represented by the target air-fuel ratio data generated by the target air-fuel ratio data generating means, depending on operating conditions of the multicylinder internal combustion engine, and the algorithm performed by the estimating means uses the target combined air-fuel ratio data generated by the target combined air-fuel ratio data generating means, the apparatus further comprises second filter means for sequentially determining actually used target combined air-fuel ratio data as target combined air-fuel ratio data corresponding to an actual target air-fuel ratio by effecting a filtering process identical to the filtering process of the mixed model type on data representing the actual target air-fuel ratio that is actually used for the air-fuel ratio manipulating means to manipulate the air-fuel ratio in each of the cylinder groups. The estimating means comprises means for generating the data representing the estimated value of the output of the exhaust gas sensor using the actually used target combined air-fuel ratio data determined by the second filter means instead of the target combined air-fuel ratio data.
The second filter means effects the filtering process identical to the filtering process of the mixed model type on the data representing the actual target air-fuel ratio that is actually used by the air-fuel ratio manipulating means, which may not necessarily be the target air-fuel ratio data generated by the target air-fuel ratio data generating means, for thereby determining the actually used target combined air-fuel ratio data as the target combined air-fuel ratio data corresponding to the target air-fuel ratio that is actually used by the air-fuel ratio manipulating means. By using the actually used target combined air-fuel ratio data instead of the target combined air-fuel ratio data in the algorithm performed by the estimating means, the data representing the estimated value of the output of the exhaust gas sensor is generated in view of how the air-fuel ratio in each of the cylinder groups is actually manipulated by the air-fuel ratio manipulating means.
Therefore, the data representing the estimated value of the output of the exhaust gas sensor which is generated by the estimating means reflects how the air-fuel ratio in each of the cylinder groups is actually manipulated by the air-fuel ratio manipulating means. Consequently, the reliability of the data representing the estimated value is increased.
In the apparatus having the estimating means, the algorithm of the estimating means may be constructed such that the model of the equivalent exhaust system comprises a model that expresses the behavior of the equivalent exhaust system with a continues time system. However, the model of the equivalent exhaust system should preferably be a model that expresses the behavior of the equivalent exhaust system with a discrete time system.
With the behavior of the equivalent exhaust system being expressed by the discrete time system, the algorithm performed by the estimating means can be constructed easily, and can be made suitable for computer processing.
If the estimating means generates the data representing the estimated value of the output of the exhaust gas sensor after the total dead time, then the model of the air-fuel ratio manipulating system may express the behavior of the air-fuel ratio manipulating system on the assumption that the actual combined air-fuel ratio at each time point is equal to the target combined air-fuel ratio prior to the dead time of the air-fuel ratio manipulating system. Therefore, there is no difference if the model of the air-fuel ratio manipulating system is expressed by either the continuous time system or the discrete time system.
The model of the equivalent exhaust system which expresses the behavior of the equivalent exhaust system with the discrete time system comprises a model which expresses the data representing the output of the exhaust gas sensor in each given control cycle, with the data representing the output of the exhaust gas sensor in a past control cycle prior to the control cycle, and the combined air-fuel ratio data in a control cycle which is earlier than the control cycle by a dead time of the equivalent exhaust system.
With the model thus constructed, the behavior of the equivalent exhaust system, including its response delay and dead time, can appropriately be expressed by the model.
The data representing the output of the exhaust gas sensor in the past control cycle is a so-called autoregressive term, and is related to a response delay of the equivalent exhaust system. The combined air-fuel ratio data prior to the dead time of the equivalent exhaust system expresses the dead time of the equivalent exhaust system.
If the model of the equivalent exhaust system is expressed by the discrete time system and the apparatus has the first filter means for determining the combined air-fuel ratio data used in the algorithm of the estimating means, then the apparatus further comprises identifying means for sequentially identifying values of parameters to be set of the model of the system equivalent to the object exhaust system, using the combined air-fuel ratio data determined by the first filter means and the output representing the output of the exhaust gas sensor. The algorithm performed by the estimating means comprises an algorithm for using the value of the parameters identified by the identifying means in order to generate the data representing the estimated value of the output of the exhaust gas sensor.
The model of the equivalent exhaust system has parameters to be set to certain values in describing its behavior. For example, if the model is a model which expresses the data representing the output of the exhaust gas sensor in each given control cycle with data representing the output of the exhaust gas sensor in a past control cycle prior to the control cycle and the combined air-fuel ratio data in a control cycle prior to the control cycle by the dead time of the equivalent exhaust system, then coefficient parameters relative respectively to the data representing the output of the exhaust gas sensor in the past control cycle and the combined air-fuel ratio data in the control cycle prior to the dead time are included as the parameters of the model.
Since the algorithm of the estimating means is based on the model of the equivalent exhaust system, the data representing the estimated value of the output of the exhaust gas sensor is generated using the parameters of the model. For increasing the reliability of the data representing the estimated value of the output of the exhaust gas sensor, it is preferable to identify the values of the parameters of the model on a real-time basis depending on the actual behavior of the equivalent exhaust system.
If the model of the equivalent exhaust system is expressed by the discrete time system, then the parameters of the model can sequentially be identified depending on the actual behavior of the equivalent exhaust system when the first filter means uses the combined air-fuel ratio data sequentially determined from the data representing the output of each of the air-fuel ratio sensors and the data representing the output of the exhaust gas sensor.
If the apparatus has the first filter means for sequentially determining the combined air-fuel ratio data used in the algorithm of the estimating means, the identifying means sequentially identifies the parameters of the model of the equivalent exhaust system, and the estimating means sequentially generates the data representing the estimated value of the output of the exhaust gas sensor using the identified values of the parameters. Therefore, it is possible to generate the data representing the estimated value of the output of the exhaust gas sensor depending on the actual behavior of the equivalent exhaust system based on the actual behavior, from time to time, of the object exhaust system. As a result, the reliability of the data representing the estimated value is increased. The highly reliable target combined air-fuel ratio data can be generated according to the algorithm of the feedback control process constructed using the data representing the estimated value, so that the output of the exhaust gas sensor can be converged to the predetermined target value accurately and stably.
If the model is a model which expresses the data representing the output of the exhaust gas sensor in each given control cycle with data representing the output of the exhaust gas sensor in a past control cycle prior to the control cycle and the combined air-fuel ratio data in a control cycle prior to the control cycle by the dead time of the equivalent exhaust system, then the identifying means identifies at least one of the coefficient parameters, preferably all the coefficient parameters, relative respectively to the data representing the output of the exhaust gas sensor and the combined air-fuel ratio data.
The identifying means can sequentially identify the values of the parameters according to an algorithm, e.g., an identifying algorithm such as a method of least squares, a method of weighted least squares, a fixed gain method, a degressive gain method, a fixed tracing method, etc., constructed in order to minimize an error between the output of the exhaust gas sensor in the model of the equivalent exhaust system and the actual output of the exhaust gas sensor.
In the above description of the identifying means, it is premised that the algorithm of the estimating means uses the combined air-fuel ratio data determined by the first filter means. However, if the algorithm of the estimating means generates the data representing the estimated value of the output of the exhaust gas sensor using the target combined air-fuel ratio data without using the combined air-fuel ratio data determined by the first filter means, then the first filter means is associated with the identifying means, and the identifying means identifies the parameters of the model of the equivalent exhaust system.
With the identifying means as well as the estimating means being employed, the algorithm of the feedback control process for generating the target combined air-fuel ratio data may be constructed based on a model of the equivalent exhaust system determined differently from the model of the equivalent exhaust system in the estimating means. However, the algorithm of the feedback control process performed by the target combined air-fuel ratio data generating means should preferably comprise an algorithm constructed based on the model of the equivalent exhaust system, for generating the target combined air-fuel ratio data using the values of the parameters identified by the identifying means.
Because the algorithm of the feedback control process is constructed based on the model of the equivalent exhaust system determined to construct the algorithm of the estimating means, the algorithm of the feedback control process using the data representing the estimated value of the output of the exhaust gas sensor generated by the estimating means can easily be constructed. At the same time, when the algorithm of the feedback control process uses the values of the parameters of the equivalent exhaust system that are identified by the identifying means, the target combined air-fuel ratio data can be generated depending on the actual behavior of the equivalent exhaust system. That is, it is possible to generate the target combined air-fuel ratio data that is highly reliable in converging the output of the exhaust gas sensor to the predetermined target value.
In the apparatus with the estimating means, the algorithm of the feedback control process performed by the target combined air-fuel ratio data generating means comprises an algorithm for generating the target combined air-fuel ratio data in order to converge the estimated value of the output of the exhaust gas sensor which is represented by the data generated by the estimating means to the predetermined target value.
The above algorithm of the feedback control process is capable of appropriately compensating for the dead time of the equivalent exhaust system or the total dead time which represents the sum of the dead time of the equivalent exhaust system and the dead time of the air-fuel ratio manipulating system, making it possible to generate the target combined air-fuel ratio data that is highly reliable in converging the output of the exhaust gas sensor to the predetermined target value.
In the apparatus with the estimating means, as is the case with the algorithm of the feedback control process based on the model of the equivalent exhaust system described above, the algorithm of the feedback control process performed by the target combined air-fuel ratio data generating means should preferably comprise an algorithm of a sliding mode control process.
Particularly, the sliding mode control process should preferably comprise an adaptive sliding mode control process.
Specifically, the sliding mode control process has the above-mentioned characteristics. By generating the target combined air-fuel ratio data using the algorithm of the sliding mode control process, particularly the adaptive sliding mode control process, the reliability of the target combined air-fuel ratio data is increased, and hence the stability of the control process of converging the output of the exhaust gas sensor to the target value is increased.
The algorithm of the sliding mode control process employs, as a switching function for the sliding mode control process, a linear function having, as components, a plurality of time-series data of the difference between estimated value of the output of the exhaust gas sensor which is represented by the data generated by the estimating means and the predetermined target value.
With the switching function for the sliding mode control process being thus constructed, the algorithm for generating the target combined air-fuel ratio data can be constructed without the need for data representing a rate of change of the output of the exhaust gas sensor. Therefore, the reliability of the generated target combined air-fuel ratio data is high.
The algorithm of the sliding mode control process generates the target combined air-fuel ratio data in order to converge the values of a plurality of time-series data of the difference between the estimated value of the output of the exhaust gas sensor and the predetermined target value to xe2x80x9c0xe2x80x9d. Thus, it is possible to appropriately compensate for the dead time of the equivalent exhaust system or the total dead time which represents the sum of the dead time of the equivalent exhaust system and the dead time of the air-fuel ratio manipulating system.
The air-fuel ratio manipulating means should preferably comprise means for manipulating the air-fuel ratio of the air-fuel mixture combusted in each of the cylinder groups in order to converge the output of each of the air-fuel ratio sensors to the target air-fuel ratio represented by the target air-fuel ratio data generated by the target air-fuel ratio data generating means, using recursive-type feedback control means respectively for the cylinder groups.
Specifically, the recursive-type feedback control means may comprise an adaptive controller, an optimum regulator, or the like. When the air-fuel ratio of the air-fuel mixture combusted in each of the cylinder groups is manipulated for each of the cylinder groups using the above control means, the air-fuel ratio in each of the cylinder groups can be controlled at the target air-fuel ratio represented by the target air-fuel ratio data with a high ability to follow dynamic changes such as changes in the operating conditions and time-dependent characteristic changes of the multicylinder internal combustion engine. Moreover, the effect of the response delay of the multicylinder internal combustion engine can also be compensated for. Therefore, especially if the data representing the estimated value of the output of the exhaust gas sensor after the total dead time which represents the sum of the dead time of the equivalent exhaust system and the dead time of the air-fuel ratio manipulating system is generated, the reliability of the data of the estimated value can further be increased.
The recursive-type feedback control means determines a new feedback controlled quantity according to a given recursive formula containing a predetermined number of time-series data, prior to the present time, of the feedback controlled quantity of the air-fuel ratio in each of the cylinder groups, i.e., a corrective quantity for the amount of supplied fuel.
The recursive-type feedback control means should preferably comprise an adaptive controller in particular.
The above and other objects, features, and advantages of the present invention will become apparent from the following description when taken in conjunction with the accompanying drawings which illustrate a preferred embodiment of the present invention by way of example.